Sloshing and slamming oscillations in a collapsible channel flow

Stewart, Peter S.; Waters, Sarah L.; Jensen, Oliver E.; Heil, Matthias

Abstract

We consider laminar high-Reynolds-number flow through a finite-length planar channel, where a portion of one wall is replaced by a thin massless elastic membrane that is held under longitudinal tension T and subject to a linear external pressure distribution. The flow is driven by a fixed pressure drop along the full length of the channel. We investigate the global stability of two-dimensional Poiseuille flow using a method of matched local eigenfunction expansions, which is compared to direct numerical simulations. We trace the neutral stability curve of the primary oscillatory instability of the system, illustrating a transition from high-frequency ‘sloshing’ oscillations at high T to vigorous ‘slamming’ motion at low T . Small-amplitude sloshing at high T can be captured using a low-order eigenmode truncation involving four surface-based modes in the compliant segment of the channel coupled to Womersley flow in the rigid segments. At lower tensions, we show that hydrodynamic modes increasingly contribute to the global instability, and we demonstrate a change in the mechanism of energy transfer from the mean flow, with viscous effects being destabilizing. Simulations of finite-amplitude oscillations at low T reveal a generic slamming motion, in which the flexible membrane is drawn close to the opposite rigid wall before recovering rapidly. A simple model is used to demonstrate how fluid inertia in the downstream rigid channel segment, coupled to membrane curvature downstream of the moving constriction, together control slamming dynamics.

Citation

Stewart, P. S., Waters, S. L., Jensen, O. E., & Heil, M. (2010). Sloshing and slamming oscillations in a collapsible channel flow. Journal of Fluid Mechanics, 662, 288-319. https://doi.org/10.1017/s0022112010003277

• Journal Article Type: Article
• Acceptance Date: Jun 12, 2010
• Online Publication Date: Aug 25, 2010
• Publication Date: 2010-11
• Deposit Date: Aug 23, 2012
• Publicly Available Date: Aug 23, 2012
• Journal: Journal of Fluid Mechanics
• Print ISSN: 0022-1120
• Electronic ISSN: 1469-7645
• Publisher: Cambridge University Press
• Peer Reviewed: Not Peer Reviewed
• Volume: 662
• Pages: 288-319
• DOI: https://doi.org/10.1017/s0022112010003277
• Keywords: Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics
• Public URL: https://nottingham-repository.worktribe.com/output/1013283
• Publisher URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7913929
• Additional Information: Accepted for publication and has appeared in a revised form, subsequent to peer review and/or editorial input by Cambridge University Press, in: Journal of Fluid Mechanics, 662 (2010), 288-319, http://journals.cambridge.org/action/displayJournal?jid=FLM